The
word FRACTAL was first used by Benoit Mandelbrot. These are interesting
mathematical figures due to the fact that as you zoom in closer to the
middle of the figure, the pattern is just as beautiful as the outside
complexity. The first fractals described date back to the 19th century.
The most ancient fractal that is known is Cantor's dust. Peano published,
in 1890, his famous curve, followed by a similar curve, yet less well-known,
published by Hilbert in 1891.

Peano's curve

Hilbert's curve

Sierpinski
also produced a well known fractal: Sierpinski's Triangle. This was
produced in 1915.

Natural
objects, such as Britain's coast, were prominent in Mandelbrot's explanation
of fractals. Britain's coast, when examined closer, seems to get smaller
and smaller in size. Therefore, Mandelbrot stated that the coast of
Britain is infinite, a statement that is not considered literal, but
had clearly been stated by Perrin without mathematical justification.

Mathematical
functions also contributed to Mandelbrot's explanations. Fundamental
works were also explained by Besicovitch and Hausdorff. This dimension,
later, played an important role in Mandelbrot's explanation.

By
compiling all of his knowledge and the discoveries of other mathematicians.
At first, these were just scattered elments with no significant meaning.
However, Mandelbrot compiled them into many explanations about fractals
and what the mathematical explanations are behind their looks. The word
fractal was invented and has been used prominently since 1975.